How can I make text appear on the screen in the game engine when the character enters a certain area?
There are plenty of ways to achieve this. 

Your scene idea could be implemented as follows:

Cube:

Collision sensor (filter for a property the character has)
AND controller
Scene Actuator Add Overlay -> your scene with text

Remarks:


ensure the camera of the overlay scene is showing something
ensure your character can be detected (static objects are not detected!). In doubt enable Game/Show physics Visualization.